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Adiabatic Quantum Computing

In light of D-Wave's announcement, we take a look how an adiabatic quantum …

The adiabatic quantum computer is an interesting concept that seems to have gathered quite an underground following in the solid-state physics community over recent years. At its most extreme, researchers have claimed that all problems belonging to a class called 'NP-complete' can be solved in a time that scales polynomially rather than exponentially, as expected in classical computations. Although I am not really able to judge this myself, it appears that these claims either don't survive peer review or are watered down quite thoroughly before publication. A primary reason that these claims are so hotly disputed is that many quantumcomputation algorithms have been shown to be optimum—there is no way within the formal logic of the problem to solve it faster—and they can't solve NP-complete problems much faster than a classical computer. However, adiabatic quantum computing uses rather different principles, which, its proponents tell us, fall outside the formal logic and can therefore be faster.

To understand adiabatic quantum computation we need to understand a little bit about how particles are described. Generally, a particle can be considered to have some potential energy and some kinetic energy. All the possible combinations of potential and kinetic energy are described by a single entity, called the Hamiltonian. In the classical quantum computation, the particles are placed inside some sort of trap, giving them a wel-defined potential and kinetic energy—the particles each occupy a single position in the Hamiltonian. Computation then takes place by manipulating the particles' position in the Hamiltonian followed by a readout of the final position. In contrast, adiabatic quantum computation doesn't directly manipulate the particles but rather changes the shape of the Hamiltonian. More specifically, if you want to solve a problem, you define it in terms of a Hamiltonian, the minimum value of which cannot usually be found. Instead of trying to solve that problem, the Hamiltonian is exchanged for one that is solvable. The new Hamiltonian is then solved and the particles put into the now-known minimum. After this is achieved, the Hamiltonian is very slowly changed back into its original form. If everything has gone well, the particles remain in the minimum state, which now represents the solution to the hard problem we started with. As with all things in quantum mechanics, the readout of the ground state gives a probabilistic answer, and the papers I have seen suggest a 90% chance of obtaining the correct answer.

Does it work? A lot of people are working very hard to show that it does. The main contender for a real quantum computer based on this idea are rings of superconducting currents that are coupled through a junction. The current in these rings can flow clockwise, anticlockwise, or be in a superposition of both. The amount of current flowing in the rings is quantized—it only has certain values, which makes it easy to convert to a quantum bit (qubit) system, where +1 and -1 unit of current correspond to binary 1 and 0 respectively. These rings can be patterned using standard lithographic processes, making for a large number of bits, each of which are individually addressable.

There are two big problems that have to be overcome before a computer can be realized. First, a method for reading out the answer has to be designed. Second, the speed with which the Hamiltonian can be manipulated needs to be determined. The central claim of adiabatic quantum computation relies on maximizing this speed. This is not such an easy problem because the qubits cross from a classical to a quantum system during the computation, and at the crossing point, there is a very high probability of upsetting the calculation. The complexity of the ever-changing Hamiltonian means that you don't know where that transition occurs, so you have to go slow for the whole transition. If you do that, then you don't achieve the NP-complete breakthrough that is claimed. However, if the cross over can be determined before hand, then the calculation can be done very fast because the change only slows during the cross over. It seems that this might have a solution in a particular measurement technique which detects the crossing point by measuring the magnetic field produced by the qubit, allowing the change in the Hamiltonian to be slowed at the only the critical point.

There are a couple of curious things about adiabatic quantum computation that are a bit disturbing. Many of their publications have sat in the arXiv pre-print archive without making it into a peer-reviewed journal. One important paper has been noted as withdrawn, yet it is still cited on blogs at D-Wave. This makes me distrustful of the results presented in the papers, and it worries me that some authors are simply abandoning peer-reviewed publication, especially since one of the key papers is receiving a fair few citations despite remaining unpublished. If D-Wave turns out to have achieved what it claims to have, this will represent a huge failure on the part of peer-reviewed literature, and that is equally troublesome, since peer review is supposed to be open to new ideas while filtering for logic and novelty.

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Chris Lee
Chris writes for Ars Technica's science section. A physicist by day and science writer by night, he specializes in quantum physics and optics. He Lives and works in Eindhoven, the Netherlands. Emailchris.lee@arstechnica.com//Twitter@exMamaku